NPV Calculator | Net Present Value
Calculate the net present value (NPV) and profitability index of an investment.
What Is the NPV Calculator | Net Present Value?
This NPV Calculator computes Net Present Value, Internal Rate of Return (IRR), Modified IRR (MIRR), Profitability Index, payback period, and discounted payback period for any stream of future cash flows. A sensitivity table shows how NPV changes across a range of discount rates, critical for understanding project risk.
- ›IRR via Newton-Raphson: converges in up to 200 iterations for robust results even with unconventional cash flow signs.
- ›MIRR with configurable reinvestment rate: addresses the key weakness of IRR by assuming positive cash flows are reinvested at a specified rate (default = discount rate).
- ›Sensitivity analysis: NPV is computed at discount rates from (r−10%) to (r+10%) in 2.5% steps, instantly showing how sensitive the project value is to the assumed rate.
- ›Dynamic cash flow rows: add or remove years as needed; negative values for cost periods are fully supported.
- ›Decision card: a clear Accept/Reject recommendation based on the NPV sign and IRR vs. discount rate comparison.
Formula
| Metric | Formula | Decision Rule |
|---|---|---|
| NPV | −C₀ + Σ Cₜ/(1+r)ᵗ | Accept if NPV > 0; reject if NPV < 0 |
| IRR | Rate r* where NPV = 0 | Accept if IRR > cost of capital (WACC) |
| MIRR | (FV of inflows / PV of outflows)^(1/n) − 1 | Addresses IRR reinvestment rate assumption |
| PI | (NPV + C₀) / C₀ = PV of inflows / C₀ | Accept if PI > 1; useful for ranking projects |
| Payback | Year when cumulative cash flows = C₀ | Shorter is better; ignores time value |
| Disc. Payback | Year when cumulative discounted CFs = C₀ | Like payback but uses present values |
How to Use
- 1Enter the initial investment (the upfront cost at time 0, entered as a positive number).
- 2Set the discount rate, this is typically your required rate of return or WACC.
- 3Enter cash flows for each future year. Click "+ Add Year" to add more periods; "-" to remove.
- 4For MIRR, set the reinvestment rate (defaults to the discount rate if left blank).
- 5Click Calculate (or press Enter) to compute NPV, IRR, MIRR, PI, and payback periods.
- 6Review the sensitivity table to understand how NPV changes at lower and higher discount rates.
- 7Use the decision card (Accept/Reject) as a quick summary of the project viability.
Example Calculation
Example, 5-year project at 10% discount rate
NPV Sensitivity
IRR vs MIRR, when does it matter?
Understanding NPV | Net Present Value
What NPV Means for Investment Decisions
Net Present Value measures the value created (or destroyed) by an investment in today's dollars. A positive NPV means the project is expected to generate returns exceeding the required rate, it creates value. A negative NPV means the project destroys value at the assumed discount rate. NPV is considered the most theoretically sound capital budgeting method because it directly measures value creation, accounts for the time value of money, and uses the appropriate risk-adjusted discount rate.
The discount rate is central to NPV analysis. For corporations, this is usually the Weighted Average Cost of Capital (WACC), the blended cost of equity and debt financing. For individual investors, it might be the opportunity cost of capital, what you could earn in the next best alternative investment. The sensitivity table in this calculator lets you see how much NPV changes as the discount rate varies, revealing how robust the investment case is to rate uncertainty.
- ›NPV > 0: accept, investment earns more than the cost of capital.
- ›NPV = 0: breakeven, IRR exactly equals the discount rate.
- ›NPV < 0: reject, better returns available elsewhere at the same risk.
- ›Comparing mutually exclusive projects: choose the one with the highest positive NPV.
Internal Rate of Return (IRR) and Its Limitations
The IRR is the discount rate that makes NPV equal to zero, it is the project's implied rate of return. The IRR decision rule is: accept if IRR > required rate (WACC). IRR is widely used because it gives an intuitive "yield" figure that can be compared to the cost of capital. However, IRR has well-known problems when used alone:
- ›Reinvestment rate assumption: IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself, unrealistic for very high IRRs.
- ›Multiple IRRs: projects with non-conventional cash flows (sign changes) can have multiple IRRs, making the rule ambiguous.
- ›Scale insensitivity: a $1 project earning 100% IRR is "better" than a $1M project earning 30% IRR, but NPV correctly ranks the second higher.
- ›Mutually exclusive projects: IRR can rank projects differently from NPV when projects have different scales or timing.
IRR is most reliable for conventional projects (single sign change: upfront cost followed by positive inflows) evaluated independently. For project ranking and comparison, NPV and PI are superior metrics.
Modified IRR (MIRR), A More Realistic Return Estimate
MIRR addresses the reinvestment rate assumption by explicitly specifying the rate at which positive cash flows will be reinvested. The calculation has three steps: (1) bring all negative cash flows back to the present at the financing rate, (2) compound all positive cash flows forward to the end of the project at the reinvestment rate, (3) find the rate that equates these two terminal values over n periods.
When the reinvestment rate equals the discount rate (the default in this calculator), MIRR is always lower than IRR for conventional projects with positive IRR. This typically gives a more conservative and realistic estimate of the project's true return. MIRR is especially valuable in private equity and project finance where the explicit reinvestment assumption is important to model correctly.
Profitability Index and Capital Rationing
The Profitability Index (PI) = (NPV + Initial Investment) / Initial Investment = PV of all inflows / Initial Investment. PI measures value created per dollar invested. A PI > 1.0 means the project is value-creating (equivalent to NPV > 0). PI is particularly useful under capital rationing, when a firm has limited capital and must choose among several positive-NPV projects. By ranking projects by PI (value per dollar invested) rather than absolute NPV, you allocate scarce capital most efficiently.
- ›PI > 1: accept; PI < 1: reject; PI = 1: breakeven.
- ›For independent projects, PI and NPV give the same accept/reject decision.
- ›For mutually exclusive projects under capital constraints, rank by PI to maximise total portfolio NPV.
- ›PI is also called the Benefit-Cost Ratio (BCR) in public sector / infrastructure analysis.
Frequently Asked Questions
What is Net Present Value and why is it the preferred capital budgeting method?
NPV measures the total value an investment creates in today's dollars by discounting all future cash flows at the required rate of return and subtracting the initial investment. It is the preferred method because:
- ›It directly measures value creation in absolute dollar terms.
- ›It accounts for the time value of money, a dollar today is worth more than a dollar in the future.
- ›It uses a risk-adjusted discount rate that reflects the opportunity cost of capital.
- ›It correctly ranks mutually exclusive projects (unlike IRR, which can give conflicting rankings).
Finance theory (based on the Modigliani-Miller framework and modern corporate finance) consistently recommends NPV as the primary investment decision criterion. Other metrics like IRR and payback period are used as supplementary information.
When should I use IRR vs NPV to evaluate a project?
Use both, but rely on NPV for the final decision:
- ›NPV: use as the primary accept/reject criterion, especially for mutually exclusive projects.
- ›IRR: use as a communication tool, "this project returns 18%" is more intuitive than "NPV = $42,000".
- ›When IRR and NPV conflict on ranking, always follow NPV.
- ›Avoid IRR for projects with unconventional cash flows (multiple sign changes), use MIRR instead.
In practice, most CFOs and investment committees look at both NPV and IRR, using IRR as a quick filter and NPV as the ultimate decision metric. The IRR decision rule (accept if IRR > WACC) gives the correct accept/reject answer for conventional projects.
What is MIRR and when is it more appropriate than IRR?
MIRR (Modified Internal Rate of Return) corrects two key IRR problems:
- ›1. Reinvestment rate: IRR assumes intermediate cash flows reinvest at the IRR; MIRR lets you specify the actual reinvestment rate.
- ›2. Multiple IRRs: MIRR always produces a single result, even for non-conventional cash flows.
- ›MIRR is especially useful when project IRR is very high (e.g. 50%+), reinvesting at 50% is unrealistic; MIRR with a realistic 10–12% reinvestment rate gives a conservative, honest return figure.
- ›In leveraged buyouts and real estate private equity, sponsors often report MIRR to avoid overstating returns.
When evaluating projects where intermediate cash flows will realistically be reinvested at a known rate (e.g. treasury yield or WACC), MIRR is more accurate than IRR. For normal projects where IRR is near the cost of capital, IRR and MIRR are very similar.
How do I choose the right discount rate for NPV?
The discount rate should reflect the risk-adjusted opportunity cost of capital for the specific project:
- ›Corporate projects: use WACC (Weighted Average Cost of Capital), the blended cost of equity and debt.
- ›Equity-financed projects: use cost of equity from CAPM: rₑ = Rₙ + β(Rₘ − Rₙ).
- ›Riskier projects: add a risk premium to WACC (e.g. WACC + 2–5% for a new product launch vs. existing operations).
- ›Personal investments: use your personal required rate of return or opportunity cost (e.g. long-run equity market return of ~8–10%).
The NPV sensitivity table in this calculator is especially useful for checking whether the accept/reject decision changes materially at different discount rates. If NPV is positive across a wide range, the investment case is robust. If it flips negative just 2% above your base rate, the analysis is very sensitive to rate uncertainty.
What is the payback period and when should I use it?
The payback period is how long it takes for cumulative cash flows to recover the initial investment. Discounted payback uses present-value-adjusted cash flows. Both ignore cash flows after the payback point, which is a major limitation.
- ›Payback: quick liquidity/risk screening, useful when capital is scarce and you need cash back fast.
- ›Discounted payback: adds time value of money; always longer than simple payback.
- ›Neither should be the primary investment criterion, use NPV for that.
- ›Common in cash-constrained SMEs and real estate where "time to break even" is a practical constraint.
Payback period is best used as a secondary screen: if two projects have similar NPV, the one with a shorter payback period carries less liquidity risk and is often preferred in practice.
What does the NPV sensitivity table tell me about project risk?
The sensitivity table shows how NPV changes when the discount rate varies from r−10% to r+10%. This reveals two key things:
- ›The NPV at your base case discount rate and how quickly it changes with rate increases.
- ›The IRR (where NPV = 0 in the table), visible as the row where NPV transitions from positive to negative.
A project with NPV = $50,000 at 10% that becomes negative at 11% is extremely sensitive to rate assumptions, any small error in estimating the cost of capital or any rate increase destroys the investment case. A project that stays positive from 10% to 25% is very robust to discount rate uncertainty.
Sensitivity analysis is a form of stress-testing. In a full project evaluation, you would also run sensitivity on cash flow assumptions (pessimistic, base, optimistic scenarios) to build a complete risk picture.
Can NPV be negative even if all annual cash flows are positive?
Yes, NPV is negative whenever the total present value of future cash flows is less than the initial investment. This happens when:
- ›The discount rate is high relative to the cash flow returns (cost of capital exceeds the project yield).
- ›The cash flows are small relative to the upfront investment.
- ›The cash flows are back-loaded (mostly in far-future years that are heavily discounted).
- ›The project duration is short with insufficient total cash flow generation.
A negative NPV does not mean the project generates cash losses, it means the project returns less than the required rate of return. You would earn more by investing the same capital elsewhere at the required rate. For example, investing $100k at 10% returns $161k after 5 years; if this project returns only $130k total (all positive cash flows), NPV at 10% is negative because $130k in future cash flows is worth less than $100k today at a 10% discount rate.